The magnitude of the gravitational force on mass m at distance x along the axis of a very thin ring when it is at position x>0 is 4GMm/4x^2-L^2.
Every body in the universe attracts every other body with a gravitational force that decreases with distance as 1/r2. if two bodies of different masses have the same acceleration they must be feeling forces in the same ratio as their masses (so a body twice as massive feels twice the gravitational force), that is, the gravitational force of attraction a body feels must be proportional to its mass.
The gravitational field at any point P in space is defined as the gravitational force felt by a tiny unit mass placed at P.
This relation can be find out by using the formula of gravitational potential = GMm/r and further integrating on small dx length at x from the origin of the rod, we get,
U = GMm/L㏑2x-2/2x+2.
now differentiating with respect to dx, we get
F = 4GMm/4x^2-L^2.
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